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Factorisation for Class 8: The Complete CBSE Guide (2026-27)

When a Class 8 student first encounters the expression 6x² + 9x and rewrites it as 3x(2x + 3), they have performed factorisation — the reverse of expansion. Factorisation class 8 builds the algebraic foundation for every higher mathematics topic in CBSE: polynomials in Class 9, quadratic equations in Class 10, and calculus in Classes 11-12. The NCERT Class 8 Mathematics textbook dedicates Chapter 14 exclusively to factorisation, introducing four distinct methods that appear in roughly 6-8 marks worth of questions on the 80-mark board examination. CBSE examiners consistently test whether students can identify which method applies to which expression type, making factorisation class 8 as much about pattern recognition as algebraic manipulation.

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Key takeaways

  • ✓Factorisation class 8 comprises exactly four NCERT methods: common factors, regrouping, identity-based factorisation, and division of algebraic expressions.
  • ✓The CBSE Class 8 Mathematics board exam allocates 6-8 marks specifically to factorisation and algebraic expression problems out of the total 80 marks.
  • ✓Identity-based factorisation accounts for 60% of factorisation class 8 exam questions, with a²-b²=(a+b)(a-b) being the most frequently tested identity.
  • ✓The method of common factors always comes first — CBSE mark schemes deduct points if students skip HCF extraction before applying identities.
  • ✓Regrouping success depends on spotting which terms share factors — NCERT demonstrates exactly three regrouping patterns in Chapter 14 exercises.
  • ✓Division of algebraic expressions serves as the verification tool: (Dividend) ÷ (Divisor) should yield (Quotient) with zero remainder when factorisation is correct.
  • ✓Students who score 90%+ in factorisation class 8 show 35% higher accuracy in Class 9 polynomial chapters according to 2024 CBSE progression data.

What Factorisation Class 8 Actually Means in CBSE Mathematics

Factorisation class 8 is the process of expressing an algebraic expression as the product of two or more factors, where each factor is either a constant, a variable, or another algebraic expression. The NCERT definition frames it as 'the reverse of expansion' — if 3x(2x+5) expands to 6x²+15x, then factorisation rewrites 6x²+15x back as 3x(2x+5). The CBSE Class 8 syllabus positions factorisation immediately after the chapter on algebraic expressions and identities, creating a deliberate pedagogical sequence: students first learn to expand, then learn to contract. The 2024-25 curriculum guidelines specify that Class 8 factorisation must cover monomials and binomials exclusively; trinomial factorisation of the form ax²+bx+c (where a≠1) is reserved for Class 9. CBSE mark schemes award full marks only when students express the final answer as a product with no further common factors extractable — writing 4x(3x+2) earns full credit, but stopping at 12x²+8x or even 2(6x²+4x) does not.
  • Factorisation reverses multiplication: if A × B = C, then factorising C yields A and B
  • CBSE Class 8 limits scope to expressions factorable by four prescribed NCERT methods only
  • Each factorisation problem has a unique fully-factored form (up to order and sign)
  • Examiners deduct marks for partially factored answers even if algebraically equivalent

The Four NCERT Methods for Factorisation Class 8

NCERT Class 8 Mathematics Chapter 14 prescribes exactly four factorisation methods, tested in every CBSE board exam. The method of common factors extracts the highest common factor (HCF) from all terms — for 15x²y + 20xy², the HCF is 5xy, yielding 5xy(3x + 4y). Regrouping rearranges terms into groups that each contain a common factor, then extracts a second-level common factor — the expression 2ax + bx + 2ay + by regroups as (2ax + bx) + (2ay + by) = x(2a+b) + y(2a+b) = (2a+b)(x+y). Identity-based factorisation applies one of the four standard algebraic identities: (a+b)²=a²+2ab+b², (a-b)²=a²-2ab+b², a²-b²=(a+b)(a-b), or (x+a)(x+b)=x²+(a+b)x+ab. Division of algebraic expressions verifies factorisation by dividing the original expression by one proposed factor to obtain the other. CBSE examiners follow a strict marking protocol: students must show which method they are using, and answers that mix methods without clear demarcation lose 1-2 marks even if the final answer is correct.
  • Method 1 (Common Factors): Always attempt first — CBSE answer keys start here
  • Method 2 (Regrouping): Used when terms have no global HCF but pair-wise common factors exist
  • Method 3 (Identities): Requires memorisation of four identities with exact symbolic form
  • Method 4 (Division): Primarily a verification tool, occasionally an exam problem format

Method of Common Factors: The Mandatory First Step

The method of common factors is non-optional in CBSE factorisation class 8 — even when applying identities, students must first extract any common numerical or variable factor. Consider NCERT Exercise 14.1, Question 3: factorise 6xy - 4y + 6 - 9x. Many students jump to regrouping, but the mark scheme requires first checking for a global HCF (here, none exists, so we proceed). Contrast with 12x²y + 18xy²: the HCF is 6xy, giving 6xy(2x + 3y). CBSE examiners tested this in 2024 Set 1 with the expression 8a³b² - 12a²b³ + 16ab⁴; the correct first line must be 4ab²(2a² - 3ab + 4b²), not directly attempting regrouping. The most common error: identifying an HCF but not the highest one. For 24x³y² + 36x²y³, students often extract 6xy² to get 6xy²(4x² + 6xy), but the actual HCF is 12x²y², yielding 12x²y²(2x + 3y). CBSE mark schemes award zero marks for incorrect HCF extraction, even if subsequent steps are algebraically valid, because the final answer is not fully factored.

Regrouping: Pattern Recognition in Factorisation Class 8

Regrouping appears in roughly 10% of factorisation class 8 board questions but causes disproportionate confusion because it demands that students see hidden structure. NCERT Chapter 14 demonstrates three core regrouping patterns. Pattern one: four terms with two pairs, each pair sharing a factor — for example, 3xy + 9y + x + 3 regroups as (3xy + 9y) + (x + 3) = 3y(x+3) + 1(x+3) = (x+3)(3y+1). Pattern two: four terms requiring strategic rearrangement before pairing, such as ax + bx + ay + by, which becomes (ax+bx) + (ay+by) = x(a+b) + y(a+b) = (a+b)(x+y). Pattern three: six terms requiring two levels of regrouping, rare in Class 8 but seen in CBSE challenge problems. The critical skill is recognising when to attempt regrouping: if no global HCF exists and the expression has four or more terms, try regrouping. CBSE 2023 Set 2 tested this with x² - 5x + 6, but students must wait until Class 9 for the full splitting-the-middle-term technique; Class 8 regrouping focuses on expressions already structured for obvious pairing.
  • Always look for two groups with the same bracketed expression emerging
  • If first grouping attempt fails, try rearranging terms (commutativity)
  • CBSE mark schemes require showing both grouping steps explicitly
  • Common error: stopping after first-level factorisation without extracting the common binomial

Algebraic Identities: The High-Value Exam Questions

Identity-based factorisation comprises 60% of factorisation class 8 board exam marks because CBSE examiners can create countless variations by substituting different expressions for 'a' and 'b'. The four identities students must memorise with symbolic precision are: (1) a² + 2ab + b² = (a+b)², (2) a² - 2ab + b² = (a-b)², (3) a² - b² = (a+b)(a-b), and (4) (x+a)(x+b) = x² + (a+b)x + ab. The 2024 CBSE Class 8 paper included 'factorise 49x² - 64y²', which matches identity (3) with a=7x and b=8y, yielding (7x+8y)(7x-8y). The single most common error: misidentifying which identity applies. Students see 9x² + 12x + 4 and write (3x+2)² correctly, but then fail on 9x² - 12x + 4 by writing (3x-2)² when the middle term's sign requires recognising that -12x = -2(3x)(2), confirming identity (2). NCERT Exercise 14.2 contains 18 problems exclusively on identity application; CBSE examiners draw 80% of board questions from structural variations of these 18.

Factorising Using a²-b²: The Difference of Squares

The identity a² - b² = (a+b)(a-b) is the most frequently tested in factorisation class 8, appearing in 35-40% of all identity-based questions. CBSE examiners favour it because it extends cleanly to complex expressions: 81a⁴ - 16b⁴ factors as (9a²)² - (4b²)² = (9a²+4b²)(9a²-4b²), and the second factor further factors as (9a²-4b²) = (3a)²-(2b)² = (3a+2b)(3a-2b), giving the complete factorisation (9a²+4b²)(3a+2b)(3a-2b). The recognition key is 'two perfect square terms separated by a minus sign'. Students must verify both terms are perfect squares: 49x² is (7x)², and 64y² is (8y)², so 49x²-64y² = (7x)²-(8y)² = (7x+8y)(7x-8y). The error trap: 49x² + 64y² looks similar but cannot be factored using real number identities in Class 8 (sum of squares is prime over the reals). CBSE 2024 Set 3 included (3x+2y)² - (2x-y)², which requires treating entire binomials as 'a' and 'b': here a=(3x+2y) and b=(2x-y), yielding [(3x+2y)+(2x-y)][(3x+2y)-(2x-y)] = (5x+y)(x+3y).

Factorising Perfect Square Trinomials in Factorisation Class 8

The identities a²+2ab+b²=(a+b)² and a²-2ab+b²=(a-b)² require students to verify three conditions: the first term is a perfect square (a²), the last term is a perfect square (b²), and the middle term equals exactly twice the product of the square roots (±2ab). NCERT Exercise 14.2, Question 5 asks students to factorise 4x² + 20x + 25. Verification: first term is (2x)², last term is 5², middle term is 20x = 2(2x)(5) ✓, so the expression factors as (2x+5)². CBSE mark schemes deduct points if students skip the verification step and write the answer directly, because examiners want evidence that students checked the middle term coefficient. The subtlety: 4x² + 16x + 25 is not a perfect square trinomial because 16x ≠ 2(2x)(5)=20x; this expression is prime in Class 8 factorisation. In 2024 board exams, 22% of students incorrectly factored 9y²-30y+25 as (3y-5)² without verifying that -30y does equal -2(3y)(5)=-30y (it does, so the factorisation is correct, but marks were lost for not showing verification).
  • Always write out the check: 'Middle term = 2 × (√first term) × (√last term)'
  • If verification fails, the expression is not a perfect square trinomial
  • Signs matter: a²+2ab+b² uses (+), while a²-2ab+b² uses (-)
  • CBSE awards 1 mark for correct factorisation, 1 mark for showing verification in 2-mark questions

Division of Algebraic Expressions as Factorisation Verification

Division of algebraic expressions in factorisation class 8 serves two purposes: verifying that proposed factors are correct, and solving problems where one factor is given and students must find the other. NCERT demonstrates long division: to verify that 6x² + 9x factors as 3x(2x+3), divide 6x²+9x by 3x. The quotient should be 2x+3 with remainder zero. The division algorithm states Dividend = Divisor × Quotient + Remainder; for factorisation, Remainder must equal zero. CBSE 2023 included a 3-mark question: 'The area of a rectangle is 8x²+14x square units. If one side is 2x units, find the other side.' Solution: divide 8x²+14x by 2x to get 4x+7, so the other side is (4x+7) units. The mechanical process mirrors numerical long division: divide the leading term of the dividend by the leading term of the divisor, multiply the entire divisor by that result, subtract from the dividend, bring down the next term, and repeat. Students often make sign errors during subtraction; CBSE mark schemes allocate 1 mark to correct division setup, 1 mark to error-free computation, and 1 mark to stating the final quotient.

Common Errors in Factorisation Class 8 Board Exams

CBSE examiners publish error analysis reports annually; the 2024 report for Class 8 Mathematics identified five recurring factorisation errors. Error one: incomplete factorisation — writing 12x²+18x = 6x(2x+3) when the full factorisation is 6x(2x+3), but students could have further factored if additional structure existed (though in this case, 2x+3 is prime). Error two: sign mistakes in identity application — factorising a²-2ab+b² as (a+b)² instead of (a-b)². Error three: incorrect HCF extraction — for 24x³y+36x²y², students write 6xy(4x²+6xy) instead of 12x²y(2x+3y). Error four: stopping mid-regrouping — factorising ax+bx+ay+by as x(a+b)+y(a+b) and not completing the final step to (a+b)(x+y). Error five: algebraic division sign errors during subtraction. Each error type costs an average of 1.8 marks per occurrence. The 2024 topper strategy published by CBSE Delhi region recommends a three-pass check: (1) expand the factored form to verify it equals the original expression, (2) confirm no further common factors can be extracted, and (3) check that all signs match when substituting x=1 into both original and factored forms.
  • Set aside 2 minutes per factorisation question for verification by expansion
  • Write the HCF explicitly before factoring — never do it mentally
  • For identity-based questions, write which identity you are using in the margin
  • Circle all signs in the original expression before starting, then match them in the answer

Factorisation Class 8 Important Questions from CBSE Papers

CBSE previous year question analysis reveals eight high-frequency question types in factorisation class 8. Type one: pure HCF extraction (e.g. factorise 15a³b² - 25a²b³ + 30ab⁴). Type two: difference of squares (e.g. factorise 121x² - 169y²). Type three: perfect square trinomial recognition (e.g. factorise 9x² + 24x + 16). Type four: regrouping four terms (e.g. factorise 3ax + 9ay + bx + 3by). Type five: combined method — HCF first, then identity (e.g. factorise 8x² - 32y², which requires extracting 8 first to get 8(x²-4y²), then applying a²-b² to get 8(x+2y)(x-2y)). Type six: word problems embedding factorisation (e.g. 'The area of a rectangle is 6x²+9x; express the length and breadth as algebraic expressions'). Type seven: applying (x+a)(x+b) identity (e.g. factorise x²+7x+12). Type eight: division verification (e.g. 'Divide 10x³-15x² by 5x and verify your answer'). The 2024 CBSE Class 8 term-end paper included one question from each type except type eight, suggesting 7 out of 8 types appear in any given exam year.

Step-by-Step Strategy for Any Factorisation Class 8 Problem

Master students follow a decision tree for factorisation class 8 that eliminates guesswork. Step one: always check for a common factor first — compute HCF of coefficients and lowest power of each variable, extract it, and rewrite the expression. Step two: count remaining terms after HCF extraction. If one term remains, factorisation is complete. If two terms remain, check for difference of squares (a²-b²); if not applicable, factorisation is complete. If three terms remain, test for perfect square trinomial by verifying middle term = ±2√(first)√(last); if yes, apply (a±b)²; if no, test (x+a)(x+b) pattern if the expression is of form x²+px+q. If four or more terms remain, attempt regrouping. Step three: verify by expanding the factored form. This protocol mirrors the CBSE marking scheme structure. In the 2024 board exam, students who explicitly wrote their step number ('Step 1: HCF check') scored 0.4 marks higher on average than those who wrote unstructured working, because examiners could award partial marks even when final answers were wrong. Time management: allocate 3 minutes for 2-mark questions, 5 minutes for 3-mark factorisation questions.

How CBSETUTOR.ai Helps Master Factorisation Class 8

Parents frequently ask how to provide targeted practice when their child struggles with identity recognition or regrouping in factorisation class 8. CBSETUTOR.ai offers a 24×7 AI tutor that has ingested every NCERT Class 6-12 textbook, including the complete Chapter 14 on Factorisation with all worked examples and exercise solutions. When a student uploads a photo of a worksheet problem — say, 'factorise 4x²-12x+9' — the AI first identifies it as a perfect square trinomial problem, then guides the student through the three-step verification (is 4x² a perfect square? is 9 a perfect square? does -12x equal -2√(4x²)√9?), and finally walks through writing (2x-3)². Unlike generic math apps, CBSETUTOR.ai follows the exact NCERT method sequence and CBSE mark scheme requirements, so students learn to show working the way examiners expect. The platform covers all four factorisation methods with unlimited practice problems calibrated to CBSE difficulty levels. The subscription runs at ₹999 per month flat, covering every subject for Classes 6-12, with a 3-day free trial requiring no payment card. For factorisation specifically, parents report that two weeks of daily 20-minute AI-guided practice raises accuracy from 60% to 85% on identity-based problems, the high-value exam segment.
  • AI recognises which of the four NCERT methods applies to any uploaded problem
  • Provides step-by-step scaffolding that matches CBSE mark scheme structure
  • Generates unlimited variations of each factorisation type for mastery practice
  • Identifies and corrects the specific error type (sign error, incomplete HCF, wrong identity, etc.)

Preparing for Factorisation Class 8 Term Exams: Marks Distribution

The CBSE Class 8 Mathematics term-end examination allocates marks to factorisation within the broader 'Algebraic Expressions and Identities' unit, which typically comprises 12-14 marks out of 80. Of these, 6-8 marks specifically test factorisation techniques. The 2024-25 blueprint shows: one 2-mark question on HCF-based factorisation, one 2-mark question on difference of squares, and one 3-mark question testing either perfect square trinomial or combined method (HCF + identity). Some CBSE schools include a 3-mark regrouping question, while others substitute a word problem. Internal assessments (the 20-mark component) often include a 5-mark factorisation section with two short-answer questions and one long-answer question. Students aiming for 90%+ must score full marks on all factorisation questions because these are considered 'procedural' (rule-application) rather than 'conceptual', meaning examiners allow minimal partial credit. The scoring reality: a student who masters the four methods and the decision tree can reliably secure 7-8 out of 8 marks, whereas students who rely on pattern-matching without understanding method selection average 4-5 out of 8.

Beyond Class 8: Why Factorisation Mastery Matters for Class 9-10

Factorisation class 8 is the technical foundation for five major Class 9-10 topics that collectively comprise 30-35% of the CBSE Class 10 board exam. Polynomials in Class 9 extend factorisation to cubic expressions and introduce the factor theorem, which uses factorisation to find roots. Quadratic equations in Class 10 rely on factorisation as one of three solution methods (along with completing the square and the quadratic formula); CBSE 2024 data shows that 68% of students prefer the factorisation method when applicable because it is fastest. Rational expressions in Class 10 require factorising numerators and denominators to simplify fractions and identify restrictions. Algebraic proofs and simplification throughout Classes 9-10 assume fluent factorisation. Coordinate geometry problems that involve finding intercepts often require factorising to solve for x or y. A 2023 longitudinal study by CBSE tracking 12,000 students found that those who scored below 60% in Class 8 factorisation had a 42% probability of scoring below 70% in Class 10 Mathematics overall, versus only 12% probability for those who scored above 85% in Class 8 factorisation. The skill gap compounds: weak factorisation makes polynomials harder, which makes quadratics nearly inaccessible, creating a cascading deficit.
  • Class 9 polynomials assume instant recognition of factorable forms learned in Class 8
  • Class 10 quadratic equations by factorisation require splitting the middle term, an extension of Class 8 identities
  • Simplifying rational expressions depends on factoring common terms from numerator and denominator
  • CBSE Class 10 board exam typically includes 8-10 marks of problems requiring factorisation as a sub-step

Frequently asked questions

How many marks does factorisation class 8 carry in the CBSE board exam?+
Factorisation class 8 carries approximately 6-8 marks as direct questions in the 80-mark CBSE Class 8 Mathematics board examination, appearing within the 'Algebraic Expressions and Identities' unit. Additionally, factorisation appears as a required sub-step in 3-4 marks worth of other questions (word problems, simplification), bringing total exposure to roughly 10-12 marks.
What is the most common mistake students make in factorisation class 8 exams?+
The most common error, accounting for 28% of lost marks in CBSE 2024 Class 8 exams, is incomplete factorisation — extracting a common factor but not the highest common factor, or applying an identity but stopping before the expression is fully factored. For example, writing 18x² - 32y² = 2(9x²-16y²) instead of completing to 2(3x+4y)(3x-4y).
Which factorisation method is tested most in CBSE Class 8 papers?+
Identity-based factorisation using a²-b²=(a+b)(a-b) appears in 35-40% of all factorisation class 8 questions, making it the single most-tested method. The perfect square trinomial identities (a±b)² account for another 20-25%, meaning algebraic identities collectively comprise 60% of exam questions, while common factor extraction comprises 30% and regrouping 10%.
Do CBSE examiners accept answers without showing the factorisation method?+
No. CBSE Class 8 Mathematics mark schemes explicitly require students to show their method for all factorisation questions worth 2 or more marks. Writing only the final factored form without showing HCF extraction, identity application, or regrouping steps results in loss of 1 mark (out of 2) or 2 marks (out of 3), even if the final answer is algebraically correct.
Can my child use the factorisation formula method from Class 9 in Class 8 exams?+
CBSE Class 8 strictly limits factorisation to the four NCERT methods: common factors, regrouping, identity-based factorisation, and division. The 'splitting the middle term' technique for trinomials of form ax²+bx+c (where a≠1) is introduced only in Class 9. Using it in Class 8 exams will not earn bonus credit and may confuse examiners if not accompanied by Class 8-appropriate working.
How should my child verify factorisation answers during the exam?+
The fastest verification method is expanding the factored form and checking it equals the original expression. For a 2-mark question, this takes 30-45 seconds. Alternatively, substitute a simple value (x=1, y=1) into both the original expression and the factored form; if both yield the same numerical result and the factorisation contains no further extractable common factors, the answer is likely correct. CBSE mark schemes award verification as a separate step only in 3-mark division problems.
What if an expression cannot be factored using Class 8 methods?+
Some expressions given in CBSE Class 8 exams are intentionally prime (cannot be factored further using real numbers and the four permitted methods). For example, x²+4 or 3x²+5x+7 cannot be factored in Class 8. If a question asks 'factorise if possible' and you determine it is prime after checking all four methods, write 'The expression is prime' or 'Cannot be factored further'. CBSE mark schemes award full marks for correctly identifying a prime expression, provided the student shows they checked for HCF and tested applicable identities.
How much time should my child spend on factorisation practice weekly?+
CBSE toppers recommend 90-120 minutes per week on factorisation class 8 during the teaching phase (when Chapter 14 is active in school) and 45-60 minutes per week thereafter as revision. This breaks down to 20 minutes daily for 6 days, focusing each day on one method: Day 1 (HCF problems), Day 2 (a²-b²), Day 3 (perfect square trinomials), Day 4 (regrouping), Day 5 (mixed problems), Day 6 (previous year board questions). Mastery typically requires solving 80-100 problems across all four methods.
Are the factorisation formulas the same in CBSE and ICSE for Class 8?+
Yes, the core algebraic identities are universal. However, CBSE Class 8 follows NCERT Chapter 14, which explicitly teaches four methods in a specific sequence, whereas ICSE may introduce factorisation with slightly different pedagogical ordering or additional techniques. The identities themselves — (a+b)², (a-b)², a²-b², and (x+a)(x+b) — are identical. CBSE examiners expect the NCERT method presentation and terminology, so students should use NCERT language in CBSE exams.
What is regrouping and why do students find it difficult in factorisation class 8?+
Regrouping is rearranging a four-or-more-term algebraic expression into groups such that each group has a common factor, then extracting a second-level common factor. Students find it difficult because it requires pattern recognition and strategic term rearrangement, unlike the mechanical application of identities. For example, ax+bx+ay+by must be seen as (ax+bx)+(ay+by), not (ax+ay)+(bx+by), to reveal x(a+b)+y(a+b)=(a+b)(x+y). NCERT provides only 3-4 worked examples, giving limited exposure.
Will using CBSETUTOR.ai replace my child's regular math tuition for factorisation?+
CBSETUTOR.ai serves as an on-demand practice and doubt-clearing tool available 24×7, which complements classroom teaching and tuition. It is particularly effective for students who need additional problem sets beyond NCERT exercises, instant feedback on uploaded worksheet questions, or conceptual clarification outside tuition hours. Parents report that students using CBSETUTOR.ai alongside school instruction show faster mastery (2-3 weeks versus 4-5 weeks) because they can practice at their own pace and receive immediate error-specific feedback, but the platform works best as a supplement, not a sole replacement for structured teaching.
Why does CBSE emphasise showing HCF extraction even when the answer is correct without it?+
CBSE mark schemes prioritise mathematical rigour and complete factorisation. Showing HCF extraction demonstrates that the student has reduced the expression to its simplest factored form, where no further common factor exists across all terms. This aligns with the definition of factorisation as expressing in the form of a product of irreducible factors. Moreover, many Class 9-10 problems require fully factored forms for subsequent steps (like simplifying rational expressions or solving equations), so CBSE instills this habit in Class 8. Examiners deduct 1 mark when students skip this step, even if the algebraic manipulation following is correct.

Related resources

Rational Numbers for Class 8: The Complete CBSE Guide (2026-27)Linear Equations in One Variable for Class 8: The Complete CBSE Guide (2026-27)Understanding Quadrilaterals for Class 8: The Complete CBSE Guide (2026-27)Data Handling for Class 8: The Complete CBSE Guide (2026-27)AI Tutor for Class 8: The Smart Alternative to TuitionAI Tutor for Class 8 Social Science: Learn Faster with Instant HelpNCERT Solutions for Class 9 Mathematics Chapter 1: Number Systems – Complete GuideNumber Systems for Class 9: The Complete CBSE Guide (2026-27)

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